Stochastic properties of dynamical

Par : Françoise Pène
  • Nombre de pages249
  • FormatGrand Format
  • PrésentationRelié
  • Poids0.7 kg
  • Dimensions17,8 cm × 24,8 cm × 1,7 cm
  • ISBN978-2-85629-967-8
  • EAN9782856299678
  • Date de parution01/03/2023
  • CollectionCollection SMF. Cours spéciali
  • ÉditeurSociété Mathématique de France

Résumé

This book provides an introduction to the study of the stochastic properties of probability preserving dynamical systems. Only the usual knowledge of the first year of a Master's degree is required. Many reminders are given. The definitions and results are illustrated by examples anc corrected exercises. The book presents the notions of Poincaré's recurrence, of ergodicity, of mixing. It enlights also existing lonks between dynamical systems and Markov chains.
The final objective of this books is to present three methods for establishing central limit theorems in the context of chaotic dynamical systems : a first method based on martingale approximations, a second method based on perturbation of quasi-compact linear operators and a third method on decorrelation estimates.
Françoise Pène studied at the University of Rennes 1 and after being admitted to the Agrégation of Mathematics, she did a Phd thesis under the supervision of Jean-Pierre Conze. She became maîtresse de conférence at the University of Brest. She is an honorary member of the Institut Universitaires de France and is currently university professor at the University of Brest. Her main field of researxh is the study of the stochastic properties of dynamical systems with chaotic behavior (including in particular the Sinai billiard, the periodic Lorentz gas, the Bunimovich stadium billiard, billiards with corners and cusps, etc.).
She also works on probabilistic models (random walks in a random sceneries, etc.).